Question

drag each formula to the solid it correctly represents.
answer choices: drag the answer choices to the correct category over here!
rectangular prism cylinder cone sphere

Explanation:

Step1: Recall volume formulas

• Rectangular Prism: Volume \(V = l\times w\times h\) (where \(l\) is length, \(w\) is width, \(h\) is height).
• Cylinder: Volume \(V=\pi r^{2}h\) (where \(r\) is radius of the base, \(h\) is height).
• Cone: Volume \(V = \frac{1}{3}\pi r^{2}h\) (where \(r\) is radius of the base, \(h\) is height).
• Sphere: Volume \(V=\frac{4}{3}\pi r^{3}\) (where \(r\) is radius).

Step2: Match the formulas

• For Rectangular Prism: \(V = lwh\) (already given).
• For Cylinder: \(V=\pi r^{2}h\).
• For Cone: \(V=\frac{1}{3}\pi r^{2}h\).
• For Sphere: None of the given formulas \(V = \pi r^{3}\), \(V=\frac{1}{3}\pi r^{3}\), \(V = 2\pi r^{2}\), \(V=\frac{1}{3}lwh\) match the correct sphere volume formula \(V=\frac{4}{3}\pi r^{3}\). But if we assume there is a mis - writing and we consider the closest among the given, there is no correct match. However, if we just use the given options:
• Rectangular Prism: \(V = lwh\) (correct as per formula).
• Cylinder: \(V=\pi r^{2}h\).
• Cone: \(V=\frac{1}{3}\pi r^{2}h\).

Answer:

• Rectangular Prism: \(V = lwh\)
• Cylinder: \(V=\pi r^{2}h\)
• Cone: \(V=\frac{1}{3}\pi r^{2}h\)
• Sphere: None of the given formulas (if we strictly follow the provided answer - choices, but the correct formula is \(V = \frac{4}{3}\pi r^{3}\))